Question: Add the following rational expressions. $\dfrac{y^3-8y^2+13}{7y^2+25}+\dfrac{-3y+17}{7y^2+25}=$
Solution: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{y^3-8y^2+13}{7y^2+25}+\dfrac{-3y+17}{7y^2+25} \\\\ &=\dfrac{(y^3-\!8y^2+13)+(-3y+17)}{7y^2+25} \\\\ &=\dfrac{y^3-8y^2+13-3y+17}{7y^2+25} \\\\ &=\dfrac{y^3-8y^2-3y+30}{7y^2+25} \end{aligned}$ In conclusion, $\dfrac{y^3-8y^2+13}{7y^2+25}+\dfrac{-3y+17}{7y^2+25}=\dfrac{y^3-8y^2-3y+30}{7y^2+25}$